Singular Value Decomposition Let \(A\) be a real \(m\times n\) matrix \((m>n)\) of full rank. We are interested in the singular value decomposition of \(A=U\Sigma V^T\). It is known that algorithms for SVD can be derived by turning the SVD problem into an eigenvalue problem. One such approach is to find the eigenvalue decomposition of the \((m+n)\times (m+n)\) symmetric matrix \[ \begin {bmatrix} 0 & A^T\\ A & 0 \end {bmatrix}. \] Establish the connections between the singular values, left and right singular vectors of \(A\) and the eigenvalues, eigenvectors of the above matrix. You should pay particular attention to the case \(m>n\). Comment on the advantages and disadvantages of this approach compared with an approach based on the eigendecomposition of \(A^TA\).